# the rule of 72

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pages: 505 words: 142,118

A Man for All Markets by Edward O. Thorp

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To get quick approximate answers to compound interest problems like these, accountants have a handy trick called “the rule of 72.” It says: If money grows at a percentage R in each period then, with all gains reinvested, it will double in 72/R periods. Example: Your money grows at 8 percent per year. If you reinvest your gains, how long does it take to double? By the rule of 72, it takes 72 ÷ 8 = 9 years, since a period in this example is one year. Example: The net after-tax return from your market-neutral hedge fund averages 12 percent a year. You start with \$1 million and reinvest your net profits. How much will you have in twenty-four years? By the rule of 72, your money doubles in about six years. Then it doubles again in the next six years, and so forth, for 24 ÷ 6 = 4 doublings. So it multiplies by 2 × 2 × 2 × 2 = 16 and becomes \$16 million. For more on the rule of 72, see appendix C.

The return series depends on the time period and on the specific index chosen. Appendix C * * * THE RULE OF 72 AND MORE The rule of 72 gives quick approximate answers to compound interest and compound growth problems. The rule tells us how many periods it takes for wealth to double with a specified rate of return, and is exact for a rate of 7.85 percent. For smaller rates, doubling is a little quicker than what the rule calculates; for greater rates, it takes a little longer. The table compares the rule in column 2 with the exact value in column 3. The “exact rule” column shows the number that should replace 72 to calculate each rate of return. For an 8 percent return, the number, rounded to two decimal places, is 72.05, which shows how close the rule of 72 is. Notice that the number in column 4 for the exact rule should equal the column 1 return per period multiplied by the corresponding values in column 3 (actual number of periods to double), but that the column 4 figures don’t quite agree with this.

Practice in the UK adds six zeros at each stage so a billion has twelve zeros, etc. one standard deviation Standard deviation indicates the size of a typical fluctuation around an average value. to the news See Nassim Taleb’s readable and insightful book Fooled by Randomness. quick mental estimate By the rule of 72, discussed later, a 24 percent annual growth rate doubles money in about 72/24=3 years. After nine years we have three doublings, to two, then four, and finally eight times the starting value. But it actually takes about 3.22 years because the rule of 72 underestimates the doubling time more and more as rates increase beyond 8 percent. of the Alamo The story of this epic battle and the subsequent ordeals of those held captive by the Japanese is told by Eric Morris in Corregidor: The American Alamo of World War II, Stein and Day, New York, 1981, reprinted paperback, Cooper Square Press, New York, 2000.

pages: 368 words: 145,841

Financial Independence by John J. Vento

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You can truly appreciate this over time, because the outcome can be astonishing. The Rule of 72 Before I describe how to use the financial tables provided in the following pages, I would like to explain the Rule of 72, which unlocks the answer to how long it will take you to double your money. Of course, the answer to this depends on your interest rate (rate of return). Simply divide the assumed rate of return into 72. For example: • If your assumed rate of return is 10 percent, divide 10 into 72, which equals 7.2 years. • If your assumed rate of return is 5 percent, divide 5 into 72, which equals 14.4 years. So, for the purpose of this example, let us assume a rate of return of 10 percent per year and a starting point of \$25,000. Based on the Rule of 72 (see Exhibit 11.1), here’s how that amount will increase: • • • • • • c11.indd 286 In 7.2 years, that \$25,000 will double to \$50,000.

They both managed to save \$20,000, but they ended up with significantly different results when they reached the age of 65: Because Brian started 10 years later than Melanie, his savings were \$100,000 less than Melanie’s! This example verifies that time is money and that one of your most valuable financial assets is time. By getting off to an early start with your retirement savings program, you can take advantage of the power of compounding. Your annual savings have the potential of earning a rate of return, and so does your reinvested earnings. Look at the Rule of 72 in Exhibit 11.1 to see just how powerful compounding can be. This is the secret to financial independence: by letting your money work for you, eventually, you will no longer have to work to maintain your desired standard of living. If you have been finding it difficult to save money on a regular basis, implement the following savings strategies that will take money directly from your paycheck on a pre-tax basis.

pages: 335 words: 94,657

The Bogleheads' Guide to Investing by Taylor Larimore, Michael Leboeuf, Mel Lindauer

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THE MAGIC IS IN THE COMPOUNDING Most people earning \$25,000 a year believe that their only shot at becoming a millionaire is to win the lottery. The truth is that the odds of anyone winning a big lottery are less than the odds of being struck twice by lightning in a lifetime. However, the power of compound interest and the accompanying Rule of 72 illustrate how anyone can slowly transform small change into large fortunes over time. The Rule of 72 is very simple: To determine how many years it will take an investment to double in value, simply divide 72 by the annual rate of return. For example, an investment that returns 8 percent doubles every 9 years (72/8 = 9). Similarly, an investment that returns 9 percent doubles every 8 years and one that returns 12 percent doubles every 6 years. On the surface that may not seem like such a big deal, until you realize that every time the money doubles, it becomes 4, then 8, then 16, and then 32 times your original investment.

By starting 10 years earlier and making one third of the investment, Eric ends up with 29 percent more. We have all heard the old cliches: If I only knew then what I know now. We are too soon old and too late smart. 0 Youth is too precious to be wasted on the young. If you are a young person, we strongly encourage you use the leverage of your youth to make the power of compounding work for you. And if you are no longer young, it's even more important. Use the time you have to make the Rule of 72 work for you. THIS ABOVE ALL: SAVING IS THE KEY TO WEALTH As you will soon learn, the Boglehead approach to investing is easy to understand and easy to do. It's so simple that you can teach it to your children, and we urge you to do so. For most people the most difficult part of the process is acquiring the habit of saving. Clear that one hurdle, and the rest is easy. What's that? You want an investment system where you don't have to save and can get rich quickly?

pages: 357 words: 91,331

I Will Teach You To Be Rich by Sethi, Ramit

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When you send money to your Roth IRA account, it just sits there. You’ll need to invest the money to start making good returns. The easiest investment is a lifecycle fund. You can just buy it, set up automatic monthly contributions, and forget about it. (If you really want more control, you can pick individual index funds instead of lifecycle funds, which I’ll discuss on page 188.) The Rule of 72 * * * The Rule of 72 is a fast trick you can do to figure out how long it will take to double your money. Here’s how it works: Divide the number 72 by the return rate you’re getting, and you’ll have the number of years you must invest in order to double your money. (For the math geeks among us, here’s the equation: 72 ÷ return rate = number of years.) For example, if you’re getting a 10 percent interest rate from an index fund, it would take you approximately seven years (72 ÷ 10) to double your money.

The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk by William J. Bernstein

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Your inflation-adjusted portfolio expected return can be calculated as follows: 1. 25% of your portfolio in small stocks: .25 ⫻ 6% ⫽ 1.5% 2. 25% of your portfolio in large stocks: .25 ⫻ 4% ⫽ 1.0% 3. 50% of your portfolio in bonds: .5 ⫻ 3% ⫽ 1.5% Thus, the real long-term expected return of your portfolio is: 1.5% ⫹ 1% ⫹ 1.5% ⫽ 4% This means that you will about double the real value of your portfolio every 18 years. (This is easily calculated from “the rule of 72,” which says that the return rate multiplied by the time it takes to double your assets will equal 72. In other words, at 6% return your capital will double every 12 years.) Take another break. Don’t look at this book for at least a few more days. In the next chapter we shall explore the strange and wondrous behavior of portfolios. Summary 1. Risk and reward are inextricably intertwined. Do not expect high returns without high risk.

pages: 670 words: 194,502

The Intelligent Investor (Collins Business Essentials) by Benjamin Graham, Jason Zweig

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) * This figure, now known as the “dividend payout ratio,” has dropped considerably since Graham’s day as American tax law discouraged investors from seeking, and corporations from paying, dividends. As of year-end 2002, the payout ratio stood at 34.1% for the S & P 500-stock index and, as recently as April 2000, it hit an all-time low of just 25.3%. (See www.barra.com/ research/fundamentals.asp.) We discuss dividend policy more thoroughly in the commentary on Chapter 19. * Why is this? By “the rule of 72,” at 10% interest a given amount of money doubles in just over seven years, while at 7% it doubles in just over 10 years. When interest rates are high, the amount of money you need to set aside today to reach a given value in the future is lower—since those high interest rates will enable it to grow at a more rapid rate. Thus a rise in interest rates today makes a future stream of earnings or dividends less valuable—since the alternative of investing in bonds has become relatively more attractive

* Today’s defensive investor should probably insist on at least 10 years of continuous dividend payments (which would eliminate from consideration only one member of the Dow Jones Industrial Average—Microsoft—and would still leave at least 317 stocks to choose from among the S & P 500 index). Even insisting on 20 years of uninterrupted dividend payments would not be overly restrictive; according to Morgan Stanley, 255 companies in the S & P 500 met that standard as of year-end 2002. † The “Rule of 72” is a handy mental tool. To estimate the length of time an amount of money takes to double, simply divide its assumed growth rate into 72. At 6%, for instance, money will double in 12 years (72 divided by 6 = 12). At the 7.1% rate cited by Graham, a growth stock will double its earnings in just over 10 years (72/7.1 = 10.1 years). * Graham makes this point on p. 73. † To show that Graham’s observations are perennially true, we can substitute Microsoft for IBM and Cisco for Texas Instruments.

pages: 416 words: 118,592

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing by Burton G. Malkiel

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Your \$100 grows to \$110 at the end of year one. Next year, you also earn 10 percent on the \$110 you start with, so you have \$121 at the end of year two. Thus, the total return over the two-year period is 21 percent. The reason it works is that the interest you earn from your original investment also earns interest. Carrying it out in year three, you have \$133.10. Compounding is powerful indeed. A useful rule, called “the rule of 72,” gives you a shortcut way to find out how long it will take to double your money. Take the interest rate you earn and divide it into the number 72, and you get the number of years it will take to double your money. For example, if the interest rate is 15 percent, it takes a bit less than five years for your money to double (72 divided by 15 = 4.8 years). The implications of various growth rates for the size of future dividends are shown in the table below.

pages: 407 words: 114,478

The Four Pillars of Investing: Lessons for Building a Winning Portfolio by William J. Bernstein

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For example, at the height of the market froth in the spring of 2000, the three companies mentioned in the last paragraph sold at 48, 84, and 67 times earnings, respectively—from three to four times the valuation of a typical company. This means the market expected these companies to eventually increase their earnings relative to the size of the market to three or four times their current proportion. This is a tricky concept. Let us assume that the stock market grows its earnings at 5% per year. This means that over a 14-year period, it will approximately double its earnings. (This is according to the “Rule of 72,” which states that the earnings rate times the doubling time equals 72. In the above example, 72 divided by 5% is approximately 14. Or, alternatively, at a 12% growth rate, it takes only six years to double earnings.) If a glamorous growth company is selling at four times the P/E ratio of the rest of the market—say, 80 times earnings versus 20 times earnings—then the market is saying that during this same 14-year period, its earnings will grow by a factor of eight (4 × 2 = 8).

pages: 386 words: 122,595

Naked Economics: Undressing the Dismal Science (Fully Revised and Updated) by Charles Wheelan

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From 1947 to 1975, productivity grew at an annual rate of 2.7 percent a year. From 1975 until the mid-1990s, for reasons that are still not fully understood, productivity growth slowed to 1.4 percent a year. Then it got better again; from 2000 to 2008, productivity growth returned to a much healthier 2.5 percent annually. That may seem like a trivial difference; in fact, it has a profound effect on our standard of living. One handy trick in finance and economics is the rule of 72; divide 72 by a rate of growth (or a rate of interest) and the answer will tell you roughly how long it will take for a growing quantity to double (e.g., the principal in a bank account paying 4 percent interest will double in roughly 18 years). When productivity grows at 2.7 percent a year, our standard of living doubles every twenty-seven years. At 1.4 percent, it doubles every fifty-one years.